Then on your master page template, make a modification to it. Place a webpart zone where the modal code goes. Then in that webpart zone add the "biz form" webpart and select the form you want to show. In the content before and after add the modal wrapping div code. Then finally at the bottom of the webpart, check the box to add an update panel around the webpart.
If you follow these directions, what may happen is your modal code may get wrapped inside the update panel. This is not ideal. The reason I suggested doing it this way first is so you can properly configure the webpart. If you have your modal code in the template and try to add a webpart to that zone, it won't work because the modal area will be hidden by default. So once you've configured your webpart, remove the content before and after from the webpart and add it back to the template around that web part zone.